Problem: Simplify to lowest terms. $\dfrac{40}{64}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 64? $40 = 2\cdot2\cdot2\cdot5$ $64 = 2\cdot2\cdot2\cdot2\cdot2\cdot2$ $\mbox{GCD}(40, 64) = 2\cdot2\cdot2 = 8$ $\dfrac{40}{64} = \dfrac{5 \cdot 8}{ 8\cdot 8}$ $\hphantom{\dfrac{40}{64}} = \dfrac{5}{8} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{40}{64}} = \dfrac{5}{8} \cdot 1$ $\hphantom{\dfrac{40}{64}} = \dfrac{5}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{64}= \dfrac{2\cdot20}{2\cdot32}= \dfrac{2\cdot 2\cdot10}{2\cdot 2\cdot16}= \dfrac{2\cdot 2\cdot 2\cdot5}{2\cdot 2\cdot 2\cdot8}= \dfrac{5}{8}$